In Figure REF ,
we also show the satellite number at different redshifts based on
the CSMF of [1]}. The satellite
number for \(\log {M_{\rm h, A}/\, h^{-1}{\rm M_\odot }}=12\) 
is close to unity for different redshifts,
consistent with the weak redshift dependence of
the host halo mass of AGNs [2]}.
Since the interaction time scale is expected to be proportional to halo dynamical time,
\(t_{\rm it}\)  is expected to decrease with increasing redshift. Moreover, galaxies at high redshift
are expected to contain more cold gas
than the low-\(z\)  counterparts.
These two factors together may lead to much
stronger and more frequent AGN activities,
which may be relevant to quasars observed at high redshift.
